3.5 Dissipation of plasma waves in solar corona and solar wind

It is now widely recognised that in the solar corona and solar wind plasma waves play a role similar to
collisions in ordinary fluids. In the expanding inhomogeneous solar wind particle distributions will develop
velocity-space gradients and strong deviations from Maxwellians, which may drive all kinds of plasma
instabilities, and thus lead to wave growth or damping. The kinetic wave modes of primary importance are
the ion-cyclotron, ion-acoustic and whistler-mode waves, which are the high-frequency extensions of such
fluid modes as the Alfvén, slow and fast magnetoacoustic waves. They will in much detail be discussed
later.

Unfortunately, we know nothing about plasma wave spectra in the corona. Therefore, in kinetic models
assumptions have to be made about the spectrum of the waves injected at the coronal base. A power-law is
often assumed, the intensity of which is then constrained by extrapolation of the in situ measurements (Tu
and Marsch, 1995) to the corona. Furthermore, the important questions of cascading - oblique as well as
parallel - remains an open problem (Cranmer and van Ballegooijen, 2003). Large-scale MHD structures
may preferentially excite perpendicular short-scale fluctuations Leamon et al. (2000), the dissipation
of which may involve strong Landau damping coupled to kinetic processes acting on oblique
wavevectors.

The relevant typical wavenumber, , for collisionless dissipation was estimated by Gary (1999), who
defined it to be the minimum value at which kinetic damping becomes significant, and determined
from linear Vlasov theory for the Alfvén-cyclotron and magnetosonic wave branches. Essentially, the
dissipation scale is set by the ion inertial length, whereby a scaling law was found to apply as follows:

Here and are fitting parameters, with being of order unity, respectively, ranges
between 0.3 (Alfvén wave) and 0.8 (magnetosonic mode). The cyclotron damping of Alfvén-cyclotron
fluctuations increases monotonically with increasing , whereas proton cyclotron damping of
magnetosonic fluctuations is essentially zero at low and becomes significant only at .
Concerning the spectral index of magnetic fluctuations in the solar wind, Li et al. (2001) argued
that collisionless dissipation, because of its exponential dependence of the damping rate on
, cannot be the main mechanism for spectral steepening; rather, damped power spectra
should decrease more rapidly than any power law as the wavenumber increases. They obtained
an analytic expression for the damping rate of the form (with fit parameter, ):

The three fit parameters depend upon and vary with the propagation angle of the waves and different values
of the plasma beta.

For the subsequent theoretical sections of this review, we provide some frequently used
definitions. The density of species is , its mass , and its plasma frequency is denoted
as . The particle’s gyrofrequency, carrying the sign of the charge, reads
, for a background magnetic field of magnitude . The mean thermal
speed is , with the temperature . The plasma beta of species is
defined as . The mass density is , and fractional mass density,
, with the total mass density being . We will also make use of the relation
, where the Alfvén speed is based on the total mass density and as usually defined by
.

Whatever the wave dissipation process heating the particles may be, it certainly must be more effective
for heavy ions than for protons (and electrons), because, as we previously discussed, the minor heavy ions
are much hotter than the protons in coronal holes and the fast solar wind (Marsch, 1991a,b; von Steiger
et al., 1995). Before we can address wave-particle interactions in more detail, the basics of kinetic theory
first need to be discussed. We return to the topic of plasma waves at a later stage of this review in
Section 5.